| 释义 |
- Images
- Symmetry
- Related polyhedra and tiling
- References
- See also
- External links
{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U74_012}}In geometry, the truncated tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of tr{4,7}. ImagesPoincaré disk projection, centered on 14-gon: SymmetryThe dual to this tiling represents the fundamental domains of [7,4] (*742) symmetry. There are 3 small index subgroups constructed from [7,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors. {{-}}| Small index subgroups of [7,4] (*742) | | Index | 1 | 2 | 14 |
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| Diagram |
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Coxeter
(orbifold) | node_c1|7|node_c1|4|node_c2
(*742) | +] = {{CDD>node_c1|7|node_c1|4|node_h0 = {{CDD|node_c1|split1-77|nodeab_c1
(*772) | +,4] = {{CDD>node_h2|7|node_h2|4|node_c2
(7*2) | node_g|7|3sg|node_g|4|node_c2
(*2222222) |
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| Index | 2 | 4 | 28 |
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| Diagram | |
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Coxeter
(orbifold) | + = {{CDD>node_h2|7|node_h2|4|node_h2
(742) | [7+,4]+ = {{CDD|node_h2|7|node_h2|4|node_h0 = {{CDD|node_h2|split1-77|branch_h2h2|label2
(772) | + = {{CDD>node_g|7|3sg|node_g|4|node_h2
(2222222) |
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Related polyhedra and tiling {{Order 7-4 tiling table}}{{Omnitruncated4 table}}{{Omnitruncated_symmetric_table}}References- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, {{isbn|978-1-56881-220-5}} (Chapter 19, The Hyperbolic Archimedean Tessellations)
- {{Cite book|title=The Beauty of Geometry: Twelve Essays|year=1999|publisher=Dover Publications|lccn=99035678|isbn=0-486-40919-8|chapter=Chapter 10: Regular honeycombs in hyperbolic space}}
See also{{Commonscat|Uniform tiling 4-8-14}}- Uniform tilings in hyperbolic plane
- List of regular polytopes
External links - {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
- {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
{{Tessellation}}{{geometry-stub}} 4 : Hyperbolic tilings|Isogonal tilings|Truncated tilings|Uniform tilings |